Q17 of 31 Page 94

Two molecules of a gas have speeds of 9 X 106 m s-1 and 1 X 106 ms-1 , respectively. What is the root mean square speed of these molecules?

Given:


Velocity of first molecule=


Velocity of second molecule=


If the number of molecules in a gas sample are n , each having speeds respectively , then the root mean square speed of these molecules is given by



Therefore, for the given question,



Putting the values we get





Therefore, root mean square speed of these molecules is


More from this chapter

All 31 →
15

The volume of a given mass of a gas at 27°C, 1 atm is 100 cc. What will be its volume at 327°C?

 16

The molecules of a given mass of a gas have root mean square speed of 100 ms -1 at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?

 18

A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system. (Oxygen has two rotational modes.)

 19

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1A and 2 A. The gases may be considered under identical conditions of temperature, pressure and volume.